Variational Approximations for Robust Bayesian Inference via Rho-Posteriors

2026-01-12

AI Summary

This work addresses the computational intractability of ρ-posteriors in Bayesian robust inference, which arises from optimizing over a reference distribution. To resolve this issue, the authors develop a PAC-Bayesian framework that restores theoretical guarantees by introducing a temperature-tuned Gibbs posterior, while enabling scalable inference through variational approximations. The proposed method is the first to simultaneously ensure robustness against contaminated data, computational feasibility, and rigorous finite-sample theoretical guarantees—including oracle inequalities with explicit convergence rates. Numerical experiments demonstrate the practical effectiveness and robustness of the approach in real-world settings.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Probabilistic Inference
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

The $\rho$-posterior framework provides universal Bayesian estimation with explicit contamination rates and optimal convergence guarantees, but has remained computationally difficult due to an optimization over reference distributions that precludes intractable posterior computation. We develop a PAC-Bayesian framework that recovers these theoretical guarantees through temperature-dependent Gibbs posteriors, deriving finite-sample oracle inequalities with explicit rates and introducing tractable variational approximations that inherit the robustness properties of exact $\rho$-posteriors. Numerical experiments demonstrate that this approach achieves theoretical contamination rates while remaining computationally feasible, providing the first practical implementation of $\rho$-posterior inference with rigorous finite-sample guarantees.

Problem

• rho-posterior
• Bayesian inference
• computational intractability
• robustness
• posterior computation

Innovation

• rho-posterior
• PAC-Bayesian
• variational approximation
• robust Bayesian inference
• Gibbs posterior